Method for the computer generation of developments

ABSTRACT

TION. THE PROJECTION IS SHIFTED AND ROTATED SO THAT THE TRUE SHAPE PROJECTION LIES TANGENT TO THE TRUE SHAPE PROJECTION OF SURFACE HAVING THE IDV(N)=1. THERE ARE THEN FOUND ALL SURFACES ADJACENT TO THE LAST-NAMED FOUND SURFACE AND IF IDV(N)=-1 FOR THESE SURFACES, THEIR IDV(N) STATES ARE SET TO 0. THE LIST OF SURFACES IS CONTINUED THROUGH UNTIL A SURFACES IS ENCOUNTERED HAVING AN IDV(N)=O, THUS INDICATING THAT IT MUST BE ADJACENT TO A PREVIOUSLY DEVELOPED SURFACE. SUCH ENCOUNTERED SURFACE IS ALIGNED WITH A PREVIOUSLY DEVELOPED SURFACE AND IN THIS POSITION THE SURFACE&#39;&#39;S DEVELOPMENT IS TESTED TO INSURE THAT IT DOES NOT OVERLAP OR INTERFERE WITH A PREVIOUSLY DEVELOPED SURFACE. THE METHOD IS INTERATIVELY PASSED THROUGH UNTIL ALL SURFACES REACH AN IDV(N)=1 STATE TO ENABLE THE DRAWING OF THE DEVELOPED OF THE THREE DIMENSIONAL OBJECT.   THE METHOD FOR COMPUTER DEVELOPING A THREE DIMENSIONAL OBJECT WHEREIN THE DEVELOPMENT STATE OF EACH PLANE SURFACE ON THE OBJECT IS DEFINED AS IDV(N) WHEREIN N IS THE SURFACE LABEL. THERE IS FIRST READ INTO THE COMPUTER&#39;&#39;S MEMORY A VERTEX LIST AND A TOPOLOGICAL MAP WHICH DESCRIBES THE OBJECT AND THEN THE EQUATIONS OF THE PLANAR SURFACES ON THE OBJECT ARE CALCULATED, THE EQUATION TAKING THE FORM AX+BY+CZ+D=O, THE COEFFICIENTS A, B, AND C ALSO BEING THE DIRECTION COSINES OF A LINE PERPENDICULAR TO THE SURFACE. THERE IS NEXT CALCULATED THE ORTHOGRAPHIC PROJECTION OF EACH SURFACE IN THE DIRECTION OF THE SURFACE NORMAL. THEREAFTER, ALL SURFACES ADJACENT TO A FIRST SURFACE BEING PROCESSED ARE FOUND. THE TERM IDV (1) IS TAKEN TO EQUAL 1 AND THE TERM IDV(N) FOR ALL SURFACES ADJACENT TO SURFACE 1 IS SET 0. AT THIS JUNCTURE, A LIST OF SURFACES IS GONE THROUGH TO FIND THE SURFACE WHICH HAS A DEVELOPMENT STATE IDV(N)=0, THE TRUE SHAPE OF WHICH IS DERIVED FROM THE ORTHOGRAPHIC PROJEC-

DEFENSIVE PUBLICATION UNITED STATES PATENT OFFICE Published at the request of the applicant or owner in accordance with the Notice of Dec. 16, 1969, 869 0.G. 687. The abstracts of Defensive Publication applications are identified by distinctly numbered series and are arranged chronologically. The heading of each abstract indicates the number of pages of specification, including claims and sheets of drawings contained in the application as originally filed. The files of these applications are available to the public for inspection and reproduction may be purchased for 30 cents a sheet.

Defensive Publication applications have not been examined as to the merits of alleged invention. The Patent Oflice makes no assertion as to the novelty of the disclosed subject matter.

PUBLISHED JULY 10, 1973 912 O.Gr. 401

SURFACES 3 l 5 s'iiilttt 9.

menu! The method for computer developing a three-dimensional object wherein the development state of each plane surface on the object is defined as IDV(N) wherein N is the surface label. There is first read into the computer's memory a vertex list and a topological map which describes the object and then the equations of the planar surfaces on the object are calculated, the equation taking the form Ax+By+Cz+D=0, the coefficients A, B, and C also being the direction cosines of a line perpendicular to the surface. There is next calculated the orthographic projection of each surface in the direction of the surface normal. Thereafter, all surfaces adjacent to a first surface being processed are found. The term IDV(1) is taken to equal 1 and the term IDV(N) for all surfaces adjacent to surface 1 is set to 0. At this juncture, a list of surfaces is gone through to find the surface which has a development state IDV(N) =0, the true shape of which is derived from the orthographic projection. The projection is shifted and rotated so that the true shape projection lies tangent to the true shape projection of surface having the IDV(N)=1. There are then found all surfaces adjacent to the last-named found surface and if IDV(N)=-l for these surfaces, their IDV(N) states are set to 0. The list of surfaces is continued through until a surface is encountered having an IDV(N)=0, thus indicating that it must be adjacent to a previously developed surface. Such encountered surface is aligned with a previously developed surface and in this position the surfaces development is tested to insure that it does not overlap or interfere with a previously developed surface. The method is iteratively passed through until all surfaces reach an IDV(N)=1 state to enable the drawing of the development of the three dimensional object.

July 10, 1973 A. APPEL ETAL T9l2,005

METHOD FOR .THE COMPUTER GENERATION OF DEVELOPMENTS Filed June 30, 1972 18 Sheets-Sheet 2 FIG. 3A

- commonums I i TRUE SHAPES COMMON l P0|NT l FIG. 3B SURFACE3 IS UNDER DEVELOPMENT smrr REQUIRED ROTATION REQUIRED .FIG.3C

July 10, 1973 APPEL ETAL T912,005

' METHOD FOR THE COMPUTER GENERATION OF DEVELOPMENTS Filed June so, 1972 I 18 Sheets-Sheet 5 FIG'4A FIG.4B

FIG.4C

July 10, 1973 A. APPEL ETAL T912,005

METHOD FOR THE COMPUTER GENERATION 0F DEVELOPMENTS I Filed June-30, 1972 l8 Sheets-Sheet 4 FIG. 5A 55 i l g L pl {A i I SURFACES l I 1. 3&5

OVERLAP 5 sunmcu i CORRECT LAYOUT FIG. 5C

July 10, 1973 A. APPEL ET METHOD FOR THE COMPUTER GENERATION OF DEVELOPMENTS Filed June 30, 1972 FIG.6A

l8 Sheets-Sheet 5 ORDER IN'WHICH SURFACES ARE TO BE PROCESSED SURFACES 1 as ARE SKIPPED LIST SPECIFICATION FIG. 6E

FIG.'6D

18 Sheets-Shed? F I G 78 LIST SPECIFICATION A. APPEL ET AL METHOD FOR THE COMPUTER GENERATION 0F DEVELOPMENTS July 10, 1973 filed June 30, 1972 FIG.7D

FIG.7C

July 10, 1973 A. APPEL ET AL METHOD FOR THE COMPUTER GENERATION 0F, DEVELOPMENTS Filed June' 30, 1972 18 Sheets-Sheet 7 FIG. 8A

FIG. as

C 8 G F July 10, 1973 I A. APPEL. ETAL T912305 METHOD FOR THE COMPUTER GENERATION 01- DEVELOPMENTS Filed June 30, 1972 18 Sheets-Sheet 8 r a T or H 2 TRUE LENGTH or 12 TYPICAL ARC 0F REVOLUTION TRUE SHAPE OF 1,2,A,D

July 10, 1973 A APPEL ET AL I T912,005

METHOD FOR THE COMPUTER GENERATION 0F DEVELOPMENTS Filed June 30, 1972 I 18 Sheets-Sheet 9 PIECE I F I I I I I FIG. [10A PIECE 1 FIG. 10C

PIECE 2 FIG. 10D

July 10, 1973 A. APPEL A METHOD FOR THE COMPUTER GENERATION OF DEVELOPMENTS Filed June 30, 1972 FIG. 11A

FIG. I1

FIG. 11F

READ NNID 52 ENTRY 20 T READ scALE FACTOR ,34 FOR DEVELOPMENT 22 READ vERTEx LIST I zas AND sTDRE 24 LsLD NNID? /58 READ TOPOLOGICAL MAP AND .sTDRE NO YE STOP 7 y cALcuLATE EDuATLDRs /26 READ 15D 0F SURFACES 28 READ A TABLE 42 CHECK To INSURE THAT 0F 10 mm ALL SURFACE EQUATION RA- RAMETERS DEscRLBE vEcToRs H g g'm'yg g'g SET IDV OF THE FIRST SURFACE IN THE DEVELOPMENT TABLE T01 FORM TABLE OF SURFACES ()N /50 SET IDV OF ALL OTHER SURFACES IN WHICH EACH EDGE OF THE THE DEVELOPMENT TABLE T0 -1 OBJECT LIES A y 18 Sheets-Sheet 1O July 10, 1973 A. APPEL T AL Filed June 30, 1972 18 Sheets-Sheet 11 Y FIG. 11B ITRY 0 ITRY ITRY+1 50 IS ITRY ITRYMAX? 52 lbw YES PRINT ERROR MESSAGE /54 NI-NI+1 |SNI ISD? has no 62 I -I0(-I) IS SURFACE I THE FIRST SUR- FACE IN THE DEVELOPMENT TABLE AND 1s ITRY =1 es- IS IDV(I)=0? Mir) YES YES July 10, 1973 APP L ETAL T912,005

METHOD FOR THE COMPUTER GENERATION OF DEVELOPMENTS Filed June 30, 1972; 18 Sheets-Sheet12 CALCULATE THE ORTHOCRAPHIC PROJECTION OF SURFACEI IN THE DIRECTION OF ITS ASSOCIATED INWARD POINTING NORMAL VEC- TOR. SCALE THE SIZE OF THE ORTHOCRAPHIC PROJECTION IN ACCORDANCE WITH THE INPUT SCALE FACTOR.

FIG.IIC

TOW. OF SURFACE I AS THE IMAGE OF SURFACE I ON THE DEVELOP- MENT PLANE 72 FORM A LIST OF ALL THE EXTERIOR EDCES OF SURFACE I 74/ IS SURFACE I THE FIRST SURFACE I IN THE DEVELOPMENT TABLE YES IS ITRY=1 YES N0 80 r I I K-ID2(NI) 82v J-J+1 9o K I FIND EDGE JON SURFACE I WHICH IS IS J JMAX V THE common EDGE OF SURFACES 1 ANDK STORE THE ORTHOCRAPIC PROJECTION I July 10, 1973 AppEL ET AL TQ'IZOOS METHOD Eon TEE COMPUTER GENERATION 0F DEVELOPMENTS I 18 Sheets-Sheet 15 Filed June 50, 1972 I 86 94 m J1 ENDPO|NT10FEDGEJ EDGE J J2--ENDPOINT 2 OF EDGE J J2--ENDPOINT2 0F EDGE J 92 v FIND SURFACE x ou THE OBJECT WHICH HAS A LINE WITH ENDPOINTS J1 AND J2 j FIG. 11D IS IDV(K)=1? YES NO CALCULATE THE SHIFT VECTOR FOR POINT J1 ON THE DEVELOP- 100 MENT PLANE IMAGE OF SURFACE I AND POINT J1 ON THE OEVEL OPMENT PLANE IMAGE OF SUR- FACE K ADD THE SHIFT VECTOR TO EACH POINT ON THE DEVELOPMENT IMAGE OF SURFACE I.

Dy (Pi, I)- Dy (Pi, I)+ Sy poms Pi ONI July 10, 1973 L J A. APPEL ETAL T912,005

METHOD FOR THE COMPUTER GENERATION OF DEVELOPMENTS Filed June 30, 1972 18 Sheets-Sheet 14 HROTATE EACH POINT on THE DEVELOPMENT PLANE IMAGE OF SURFACE I BY ANGLE -A.

108x DOES THE DEVELOPMENT PLANE IMAGE OF SURFACE I- OVERLAP THE DEVELOPMENT PLANE IMAGE OF ANY OTHER PREVIOUSLY DEVELOPED SURFACE no YES 1 T FIG. 11E 110- mmfl I PM my IS J JMAX NO YES 12 11a. J1 ENDPOINTT OF DOES NHSD? EDGE J YES L N0 IEND-0 12 E, J2 ENDPOINT 20F 12a EDGEJ 1E-0-1ENO 1 -/130 July 10, 1973 A. APPEL ET AL METHOD FOR THE COMPUTER GENERATION OF DEVELOPMENTS Filed June 30, 1972 18 Sheets-$heet 15 IS IEND ISD JI AND J2 mum-*0 YES REPOSITION THE DIGITAL PLOTTER PEN YES RENDER ON THE DIGITAL PLOTTER THE DEVELOPMENT PLANE IMAGES OF ALL SURFACES IN THE CURRENT DEVELOP- NENT LIST.

July 10, 1973 A. APPEL ET AL T9l2,005

METHOD FOR THE COMPUTER GENERATION OF DEVELOPMENTS Filed June 30, 1972 18 SheetsSheet 16 /RESULT Fl G 13B TYPICAL PERPENDICULAR;

TRUE SHAPE OF ORTHOGRAPHIC SURFACE I PROJECTION PLANE E July 10, 1973 APPEL ET AL METHOD FOR THE COMPUTER GENERATION OF DEVELOPMENTS Filed June 30, 197.2 18 Sheets-Sheet 17 THE o'msm PROJECTION 0F F I G 1 5A DEVELOPMENT PLANE DPI2 F I G 1 5B July 10, 1973 APPEL ET AL T912,005

METHOD FOR THE COMPUTER GENERATION OF DEVELOPMENTS Filed June 30, 1.972 18 Sheets-Sheet 18 FIG.17A

I EDGEJ J2 \SURFACEKISADJACENT TOSURFACEI DX(J1,K)

- DEVELOPMENT PLANE HQH SHIFT VECTOR DYUIK) \\4\ MI NJJWICQNDJLK I INCIDE 0mm A"; DX

J2,K 1 ,A ,J2,I ORIGINOF EF I DEVELOPMENTPLANE WM) J2,K J2,I

FIG.17B H6 18 /TYP|CAL souo DEVELOPMENT P6 P4 PLANE FIG. 20A

P7 J1,IANDJ1,K P2

12,1 AND J2,K NOW COINCIDE FIG. 20B

FIG.19 

